Out-of-Plane Deformations Determined Mechanics of Vanadium Disulfide (VS₂) Sheets

The rapid development of two-dimensional (2D) materials has significantly broadened the scope of 2D science in both fundamental scientific interests and emerging technological applications, wherein the mechanical properties play an indispensably key role. Nevertheless, particularly challenging is the ultrathin nature of 2D materials that makes their manipulations and characterizations considerably difficult. Herein, thanks to the excellent flexibility of vanadium disulfide (VS₂) sheets, their susceptibility to out-of-plane deformation is exploited to realize the controllable loading and enable the accurate measurements of mechanical properties. In particular, the Young's modulus is estimated to be 44.4 ± 3.5 GPa, approaching the lower limit for 2D transition metal dichalcogenides (TMDs). We further report the first measurement of thickness-dependent bending rigidity of VS₂, which deviates from the prediction of the classical continuum mechanics theory. Additionally, a deeper understanding of the mechanics within two dimensions also facilitates the modulation of strain-coupled physics at the nanoscale. Our Raman measurements showed the Grüneisen parameters for VS₂ were determined for the first time to be γ_E ≈ 0.83 and γ_A1g ≈ 0.32.